Question

This is matrix in 3x3 in row.
A={(1,2,3) , (4,5,6) , (1,2,3)}
B={(4,5,6) , (1,2,3) , (7,8,9)}
Are A and B row equivalent?

Answer 1

row reduce them to echelon form

Answer 2

I got {(1,2,3),(0,1,2),(0,0,0)} and the other also same.

Answer 3

But A and B have the same null space, are they row equivalent?

Answer 4

If you only know two matrices have the same null space, then you know that they are row equivalent.

I'm not entirely sure why, but here's where I read it: http://en.wikipedia.org/wiki/Row_equivalence#Additional_properties

Answer 5

If the first two row in row echelon form of A and B are same which is 1,2,3 and 0,1,2 but the third row both got 0,0,0 , do it count row equivalent for A and B?

Answer 6

row equivalent matrixes can be formed into each other by elementary row operations. If we can reduce them to the same echelon form, then we can just as readily revert them backwards into each other .... all invertible nxn matrixes are row equivalent since they can be reduced to the identity matrix